This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, non-linear interactions in deep water; 4, white-capping dissipation; 5, non-linear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments. Keywords

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The generalized Lagrangian mean (GLM) formulation is used to describe the interaction of waves and currents. In contrast to the more conventional Eulerian formulation the GLM description enables splitting of the mean and oscillating motion over the whole depth in an unambiguous and unique way, also in the region between wave crest and trough. The present paper deals with non-breaking long-crested regular waves on a current using the GLM formulation coupled with a WKBJ-type perturbation-series approach. The waves propagate under an arbitrary angle with the current direction. The primary interest concerns nonlinear changes in the vertical distribution of the mean velocity due to the presence of the waves, but modifications of the orbital velocity profiles, due to the presence of a current, are considered as well. The special case of no initial current, where waves induce a so-called drift velocity or mass-transport velocity, is also studied.

[1] The performance of the spectral wind wave model SWAN in tidal inlet seas was assessed on the basis of extensive wave measurements conducted in the Amelander Zeegat tidal inlet and the Dutch Eastern Wadden Sea, as well as relevant data from other inlets, lakes, estuaries and beaches. We found that the 2006 default SWAN model (version 40.51), the starting point of the investigation, performed reasonably well for measured storm conditions, but three aspects required further attention. First, over the near-horizontal tidal flats, the computed ratio of integral wave height over water depth showed an apparent upper limit using the default depth-limited wave breaking formulation and breaker parameter, resulting in an underprediction of wave heights. This problem has been largely solved using a new breaker formulation. The second aspect concerns wave-current interaction, specifically the wave age effect on waves generated in ambient current, and a proposed enhanced dissipation in negative current gradients. Third, the variance density of lower-frequency wind waves from the North Sea penetrating through the inlets into the Wadden Sea was underpredicted. This was improved by reducing the bottom friction dissipation relative to that of the default model. After a combined calibration, these improvements have resulted in a relative bias reduction in H m0 from À3% to À1%, in T mÀ1,0 from À7% to À3%, and in T m01 from À6% to À2%, and consistent reductions in scatter, compared to the 2006 default model.